Martian Data Assimilation Using the LETKF

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The Explanation of Ocean Instabilities Using
Breeding
Courtesy NOAA/AVHRR
Matthew J. Hoffman CEAFM/Burgers Symposium May 8,
2009 Johns Hopkins University
Courtesy NASA Earth Observatory
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Outline

• Overview of ocean instabilities
• Overview of the breeding method
• Application to global ocean model
• Development of bred vector energy equations to
  diagnose instability dynamics
• Study of Pacific tropical instabilities

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Ocean Instabilities
Ducet et al., 2000

• Flow Instabilities are prevalent in the upper
  ocean
• Most occur in strong currentswestern boundary
  currents, Southern Ocean
• Instabilities take place on different timescales
• Tropical Pacific instabilities are some of the
  strongest

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Pacific Tropical Instabilities
Jesse Allen, NASA Earth Observatory SST from
Advanced Microwave Scattering Radiometer on Aqua

• Pacific Tropical Instability Waves are seen in
  the Pacific equatorial cold tongue
• Periods of 20-30 days, Wavelength of 1000km
• Tropical waves are coupled to the atmospheric
  boundary layer and are important for heat and
  momentum balances
• Masina et al. (1999) argued for baroclinic energy
  conversion dominating
• Qiao and Weisberg (1995)argued for barotropic
  energy conversion dominating

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Overview of Breeding Method

• Developed by Toth and Kalnay (1993, 1997) to
  estimate the shape of growing errors in a
  non-linear atmospheric model
• Also provides initial conditions for ensemble
  forecasting
• 2 parameters in the methodrescaling size and
  time between rescaling
• Parameters can be tuned to isolate instabilities
  of different time scales
• Yang et al. (2005) used breeding on a coupled GCM
  to identify slow growing ENSO modes

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Overview of Breeding Method

• A small, random perturbation is added to the
  initial state of the system
• Both the perturbed and unperturbed (control)
  conditions are integrated forward in time
• The control forecast is subtracted from the
  perturbed forecast, yielding the bred vector
• The bred vector is rescaled to its initial size
  and added to the control forecast as a new
  perturbation

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MOM2 Global Model

• GFDL Modular Ocean Model (MOM) 2b code
• Driven by monthly averaged NCEP reanalysis winds
  from 1950-1995
• SST and surface salinity from World Ocean Atlas
  1994
• Same setup used by Carton et al. (2000) for SODA
• 1 resolution in longitude, stretched latitude
  grid ranging from 1 in midlatitudes to ½ in
  tropics
• 20 vertical levels 15 meters level thickness
  near surface

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Bred Vectors

• 10 day bred vectors identify many instabilities
  in the ocean
• Instabilities are seen in the Southern Ocean, in
  boundary currents, and in the Tropical Pacific,
  among other locations

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Tropical Pacific Bred Vectors
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Tropical Pacific Bred Vectors

• Seasonal cycle is clear
• Speed is 0.46m/s
• Wavelength is 1000km
• 25 day period

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Tropical Pacific Bred Vectors

• Seasonal cycle is clear
• Speed is 0.46m/s
• Wavelength is 1000m
• 25 day period
• Interannual cycle tied to El Niño-La Niña cycle
  (ENSO)

El Niño
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Tropical Pacific Bred Vectors

• Seasonal cycle is clear
• Speed is 0.46m/s
• Wavelength is 1000m
• 25 day period
• Interannual cycle tied to El Niño-La Niña cycle
  (ENSO)

La Niña
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Bred Vector Kinetic Energy

• Momentum Equations
• Kinetic energy defined as
• Bred kinetic energy is

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Bred Vector Kinetic Energy

• Terms have physical interpretation

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Bred Vector Kinetic Energy

• Terms have physical interpretation
• Horizontal and vertical divergence of energy
  transport

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Bred Vector Kinetic Energy

• Terms have physical interpretation
• Horizontal and vertical divergence of energy
  transport
• Work of pressure force

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Bred Vector Kinetic Energy

• Terms have physical interpretation
• Horizontal and vertical divergence of energy
  transport
• Work of pressure force
• Baroclinic conversion term

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Bred Vector Kinetic Energy

• Terms have physical interpretation
• Horizontal and vertical divergence of energy
  transport
• Work of pressure force
• Baroclinic conversion term
• Barotropic conversion term

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Bred Vector Kinetic Energy

• Tropical Pacific shows positive conversion (bred
  potential to bred kinetic)
• Shows Instability Growth
• South Atlantic shows negative conversion (bred
  kinetic to bred potential)
• Stabilizing region

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Bred Vector Kinetic Energy

• Tropical Pacific shows positive conversion (bred
  potential to bred kinetic)
• Shows Instability Growth
• South Atlantic shows negative conversion (bred
  kinetic to bred potential)
• Stabilizing region

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Bred Vector Kinetic Energy

• Tropical Pacific shows positive conversion (bred
  potential to bred kinetic)
• Shows Instability Growth
• South Atlantic shows negative conversion (bred
  kinetic to bred potential)
• Stabilizing region

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Tropical Pacific Instabilities

• Monthly averages over a 30 year period are shown
  for January
• Depth averaged over upper 150m
• Baroclinic conversion is strongest from 3N-5N
• Barotropic conversion is strongest at the equator
• Baroclinic conversion is stronger in this model
• Energy conversion is strongest when bred vectors
  are strongest (La Niña)

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Tropical Pacific Instabilities
At 3.5N
At 0.25N

• Baroclinic conversion is strongest at coldest
  temperatures (cold tongue)
• Barotropic conversion is strongest at shear
  points (between South Equatorial Current and
  Equatorial Undercurrent)
• Different locations for the different mechanisms

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Summary

• Breeding is an easy way to identify instabilities
  in a dynamical system
• Breeding energy equations allow bred vectors to
  be used to diagnose the dynamical causes of
  instabilities
• Tropical Pacific instabilities have a baroclinic
  and barotropic component
• Baroclinic component is stronger in this model
  and occurs along the north edge of the cold
  tongue between 3N and 5N
• Barotropic component occurs at the equator
  between the South Equatorial Current and the
  Equatorial Undercurrent

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• END